Sequentially laminated printed circuit boards are multilayer boards that contain blind vias. One or more sub-assemblies, for example two two-layer boards or two four-layer boards, are first drilled, plated, and patterned. Then the sub-assemblies are laminated together and the entire assembly is drilled, plated, and patterned again. The several plating steps required to plate the vias in this multiplicity of steps produces relatively thick copper on the board surfaces. This thick copper precludes the formation of fine circuit traces when using isotropic wet etching. To avoid this problem, it is common practice to reduce the copper thickness by mechanical grinding or chemical etching. Neither process is highly uniform, repeatable, or controllable. Referring now to FIG. 1, the copper can easily be reduced too much, resulting in “butt joints” 140 between the barrel 120 of the via and the surface copper 130 at the top edge of the via. Butt joints are latent defects that result in intermittent contacts or open circuits when the laminate 110 expands faster during thermal excursions than the copper plating 120, causing the two metal members to separate. This results in field failures, and it is highly desirable to eliminate this reliability risk. It would be a significant addition to the art if a multilayer printed circuit board could be fabricated that could meet strict dimensional tolerances and still have highly reliable via structures.